Classifying semi-free Hamiltonian $S^1$-manifolds

Details Classifying semi-free Hamiltonian $S^1$-manifolds Classifying semi-free Hamiltonian $S^1$-manifolds

2005-02-16

arxiv.org/abs/math/0502364v2

Mathematics

Symplectic Geometry

Many errors corrected. To appear in IMRN.

Scientific paper

In this paper we describe a method to establish when a symplectic manifold $M$ with semi-free Hamiltonian $S^{1}$-action is unique up to isomorphism (equivariant symplectomorphism). This will rely on a study of the symplectic topology of the reduced spaces. We prove that if the reduced spaces satisfy a rigidity condition, then the manifold $M$ is uniquely determined by fixed point data. In particular we can prove that there is a unique family up to isomorphism of 6-dimensional symplectic manifolds with semi-free $S^1$-action and isolated fixed points.

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